# Potential Energy

The potential energy of a system of particles is related to the system’s position measured in the direction of the gravitational force.

The potential energy of a fixed system of particles (i.e. closed system) is defined by the equation

where m is the mass, g is the gravitational acceleration, and z is the height of the system measured relative to a reference height. The potential energy is a measure of how much work was expended to raise the fluid particles. The work is equal to the weight of the fluid particles times the distance measured in a direction opposite to that of the direction of gravity. As such only the displacement in the direction of gravity is important. The fluid particles can move normal to the gravity vector without causing additional work to be done. Consequently, the potential energy is a state variable. The potential energy doesn’t depend on the path taken, only on the distance relative to its reference position.

## Learning Objectives:

Define potential energy, compute potential energy given the mass, gravitational acceleration, and reference height, and affirm that potential energy is a state variable.